Striped Twisted State in the Orientational Epitaxy on Quasicrystals

The optimal "twisted"geometry of a crystalline layer on a crystal has long been known, but that on a quasicrystal is still unknown and open. We predict analytically that the layer equilibrium configuration will generally exhibit a nonzero misfit angle. The theory perfectly agrees with numerical optimization of a colloid monolayer on a quasiperiodic decagonal optical lattice. Strikingly different from crystal-on-crystal epitaxy, the structure of the novel emerging twisted state exhibits an unexpected stripe pattern. Its high anisotropy should reflect on the tribomechanical properties of this unconventional interface.